% -- a tex file of various latex commands used throughout my thesis
% -- it's a good idea to hang onto this one for whenever the
% -- paper is latexed; i'll send updates.


\newcommand{\nc}{\newcommand}
\nc{\nn}{\nonumber}
\nc{\fns}{\footnotesize}

\nc{\revisionline}{\vspace{.1in} \today \vspace{.1in} \hrule\hrule\hrule\vspace{.1in}}
\nc{\newpp}{\vspace{.1in} \noindent}

\nc{\slideline}{\smallskip \hrule\hrule \smallskip}

\nc{\wh}{\widehat}

\def\boxit#1{\vbox{\hrule\hbox{\vrule\kern6pt
          \vbox{\kern6pt#1\kern6pt}\kern6pt\vrule}\hrule}}

% -- sensitivity and specificity
\newcommand{\se}{\text{se} }
\newcommand{\spec}{\text{sp} }
\newcommand{\fpr}{\text{{\sc fpr}}}
\newcommand{\fnr}{\text{{\sc fnr}}}

% -- probability notation
\nc{\Ef}{ {\rm E}_{\infty} }
\nc{\Ex}{ {\rm E} }
\nc{\Ec}{ {\rm E}_1 }
\nc{\Pf}{ {\rm P}_{\infty} }
\nc{\Pc}{ {\rm P}_{1} }
\nc{\Prb}{ {\rm P} }
\nc{\sd}{\pm \hat{\sigma} }

\nc{\indep}{{\, \perp \! \! \! \perp  \,} }
\nc{\tsps}{^{ {\rm T} } }



\nc{\pu}{\pi_{\rm U}}
\nc{\pbi}{\pi_{\rm B}}
\nc{\pnb}{\pi_{\rm NB}}
\nc{\prp}{\propto}
\nc{\pr}{ {\rm pr} }

% --- distributions
\newcommand{\Poi}{\text{Poi}}
\newcommand{\Bin}{\text{Bin}}
\newcommand{\Ber}{\text{Ber}}
\newcommand{\Mult}{\text{Mult}}




% -- greek letters
%\nc{\th}{\theta}
\nc{\al}{\alpha}
\nc{\dl}{\delta}
\nc{\la}{\lambda}
%\nc{\om}{\omega}
\nc{\vep}{\varepsilon}
\nc{\eps}{\epsilon}

% -- summations
\nc{\snf}{\sum_{n=1}^{\infty}}
\nc{\skf}{\sum_{k=1}^{\infty}}
\nc{\sner}{\sum_{n=1}^{86}}
\nc{\sjn}{\sum_{j=1}^{n}}
\nc{\skn}{\sum_{k=1}^{n}}
\nc{\sumim}{\sum_{i=1}^m}
\nc{\sumjn}{\sum_{j=1}^n}
%\nc{\sumlL}{\sum_{l=1}^{L_j}}
\nc{\sumlL}{\sum_{l=1}^{L}}
\nc{\sumL}{\sum_{l=1}^{L}}
\nc{\sumkK}{\sum_{k=1}^{K_i}}
\nc{\sumrR}{\sum_{r=1}^R}



\nc{\hivp}{\sum_{ {\rm HIV}^+ } }
\nc{\sumiN}{ \sum_{i=1}^N }
\nc{\summM}{ \sum_{m=1}^M }
\nc{\sumjM}{ \sum_{j=1}^M }
%\nc{\sumkK}{ \sum_{k=1}^K }


% -- grouping symbols
\nc{\lsq}{\left[}
\nc{\rsq}{\right]}
\nc{\lbc}{\left \{ }
\nc{\rbc}{\right \} }
\nc{\lp}{\left(}
\nc{\rp}{\right)}

% -- limits, etc.
\nc{\imp}{\Rightarrow}
\nc{\lbf}{\lim_{b \rightarrow \infty}}
\nc{\limNinf}{\lim_{N \rightarrow \infty}}
\nc{\limminf}{\lim_{m \rightarrow \infty}}
\nc{\limninf}{\lim_{n \rightarrow \infty}}
\nc{\convd}{\stackrel{D}{\longrightarrow}}
\nc{\convp}{\stackrel{P}{\longrightarrow}}
\nc{\eqd}{\stackrel{{\EuScript D}}{=}}


% -- special notation
\nc{\trans}{^{\text T}}
\nc{\ol}{\overline}
\nc{\logit}{\text{logit}\,}


\nc{\rl}{ {\rm {\bf R} } }
\nc{\zah}{ {\rm {\bf Z} } }

\nc{\lkn}{\Lambda^n_k}
\nc{\stp}{ {\cal C}_b }
\nc{\istp}{ {\cal I}_A }
\nc{\snb}{S_{N_b}}
\nc{\stb}{S_{T_b}}
\nc{\ixlog}{I_{ \{ 0 \leq x \leq \log \al \} } }
\nc{\iulog}{I_{ \{ 0 \leq u  \leq \log \al \} } }
\nc{\rgn}{ \Upsilon_n }
\nc{\var}{{\rm var}}
\nc{\cov}{{\rm cov}}
\nc{\corr}{{\rm corr}}
\nc{\dpl}{\partial}
\nc{\half}{ {\textstyle \frac{1}{2}} }
\nc{\tr}{{\rm trace}}
\nc{\real}{\mathbb{R}}
\nc{\bbC}{\mathbb{C}}
\nc{\bbR}{\mathbb{R}}
\nc{\bbone}{\mathbb{1}}
\nc{\bbP}{\mathbb{P}}

\def\boxit#1{\vbox{\hrule\hbox{\vrule\kern6pt\vbox{\kern6pt#1\kern6pt}\kern6pt\vrule}\hrule}}

%% --- calligraphy
\nc{\calb}{ {\cal B} }
\nc{\calc}{ {\cal C} }
\nc{\bcalc}{ \mbox{\boldmath{${\cal C}$}}}
\nc{\cald}{ {\cal D} }
\nc{\cale}{ {\cal E} }
\nc{\cali}{ {\cal I} }
\nc{\call}{ {\cal L} }
\nc{\calm}{ {\cal M} }
\nc{\caln}{ {\cal N} }
\nc{\cals}{ {\cal S} }
\nc{\calo}{ {\cal O} }
\nc{\bcalo}{ \mbox{\boldmath{${\cal O}$}}}
\nc{\calt}{ {\cal T} }
\nc{\calv}{ {\cal V} }
\nc{\bcalu}{ \mbox{\boldmath{${\cal U}$}}}
\nc{\calu}{ {\cal U} }
\nc{\calw}{ {\cal W} }
\nc{\calx}{ {\cal X} }



%% --- euscript
\nc{\sca}{ {\EuScript A} }
\nc{\scb}{ {\EuScript B} }
\nc{\scc}{ {\EuScript C} }
\nc{\scd}{ {\EuScript D} }
\nc{\sce}{ {\EuScript E} }
\nc{\scf}{ {\EuScript F} }
\nc{\scF}{ {\EuScript f} }
\nc{\scg}{ {\EuScript G} }
\nc{\sch}{ {\EuScript H} }
\nc{\sci}{ {\EuScript I} }
\nc{\scj}{ {\EuScript J} }
\nc{\sck}{ {\EuScript K} }
\nc{\scl}{ {\EuScript L} }
\nc{\sclic}{ \scl_i^{\rm c} }
\nc{\scm}{ {\EuScript M} }
\nc{\scn}{ {\EuScript N} }
\nc{\sco}{ {\EuScript O} }
\nc{\scp}{ {\EuScript P} }
\nc{\scq}{ {\EuScript Q} }
\nc{\scr}{ {\EuScript R} }
\nc{\scs}{ {\EuScript S} }
\nc{\sct}{ {\EuScript T} }
\nc{\scu}{ {\EuScript U} }
\nc{\scv}{ {\EuScript V} }
\nc{\scw}{ {\EuScript W} }
\nc{\scx}{ {\EuScript X} }
\nc{\scy}{ {\EuScript Y} }
\nc{\scz}{ {\EuScript Z} }
\nc{\scxo}{ {\EuScript X}_{\rm obs} }
\nc{\Xobs}{ \pmb{\scx}_{\rm obs} }
\nc{\Xcom}{ \pmb{\scx} }
\nc{\Xmis}{ \pmb{\scx}_{\rm mis} }

\nc{\bsci}{ \mbox{\boldmath{$\sci$}}}  
\nc{\bscj}{ \mbox{\boldmath{$\scj$}}}  

\nc{\sumlic}{\sum_{l \in sclic}}

\nc{\scyo}{ {\EuScript Y}_{\rm obs} }

% --- calligraphy
%\nc{\scb}{ {\cal B} }
%\nc{\scc}{ {\cal C} }
%\nc{\scd}{ {\cal D} }
%\nc{\sce}{ {\cal E} }
%\nc{\sch}{ {\cal H} }
%\nc{\sci}{ {\cal I} }
%\nc{\scj}{ {\cal J} }
%\nc{\sck}{ {\cal K} }
%\nc{\scl}{ {\cal L} }
%\nc{\sclic}{ \scl_i^{\rm c} }
%\nc{\scm}{ {\cal M} }
%\nc{\scn}{ {\cal N} }
%\nc{\sco}{ {\cal O} }
%\nc{\scr}{ {\cal R} }
%\nc{\scs}{ {\cal S} }
%\nc{\sct}{ {\cal T} }
%\nc{\scv}{ {\cal V} }
%\nc{\scw}{ {\cal W} }
%\nc{\scx}{ {\cal X} }
%\nc{\scxo}{ {\cal X}_{\rm obs} }
%\nc{\Xobs}{ \pmb{\scx}_{\rm obs} }
%\nc{\Xcom}{ \pmb{\scx} }
%\nc{\Xmis}{ \pmb{\scx}_{\rm mis} }
%
%\nc{\bsci}{ \mbox{\boldmath{$\sci$}}}  
%\nc{\bscj}{ \mbox{\boldmath{$\scj$}}}  
%
%\nc{\sumlic}{\sum_{l \in sclic}}
%
%\nc{\scy}{ {\cal Y} }
%\nc{\scyo}{ {\cal Y}_{\rm obs} }



% --- arrays
\nc{\bga}{\begin{array}{c}}
\nc{\ena}{\end{array}}

% --- hats
\nc{\mhat}{ {\hat{p}}_M }
\nc{\fhat}{ {\hat{p}}_F }
\nc{\ph} { \hat{p} }

% --- tildes
\nc{\ta}{ {\tilde{a}} }
\nc{\tc}{ {\tilde{c}} }

% -- boldface math
\nc{\bi}{\mbox{\boldmath{$i$}}} 
\nc{\bal}{\mbox{\boldmath{$\alpha$}}} 
\nc{\balpha}{\mbox{\boldmath{$\alpha$}}} 
%\nc{\bal}{\pmb{\alpha}}
\nc{\bone}{\mbox{\boldmath{$1$}}} 
\nc{\bbet}{\mbox{\boldmath{$\beta$}}} 
\nc{\bbeta}{\mbox{\boldmath{$\beta$}}} 
\nc{\bDel}{\mbox{\boldmath{$\Delta$}}} 
\nc{\bDelta}{\mbox{\boldmath{$\Delta$}}} 
\nc{\bdel}{\mbox{\boldmath{$\delta$}}}
\nc{\bdelta}{\mbox{\boldmath{$\delta$}}}
\nc{\bet}{\mbox{\boldmath{$\eta$}}}
\nc{\beps}{\mbox{\boldmath{$\epsilon$}}}
\nc{\bvep}{\mbox{\boldmath{$\vep$}}} 
\nc{\bgam}{\mbox{\boldmath{$\gamma$}}} 
\nc{\bgamma}{\mbox{\boldmath{$\gamma$}}} 
\nc{\bGamma}{\mbox{\boldmath{$\Gamma$}}} 
\nc{\boldeta}{\mbox{\boldmath{$\eta$}}} 
\nc{\bLam}{\mbox{\boldmath{$\Lambda$}}} 
\nc{\bLambda}{\mbox{\boldmath{$\Lambda$}}} 
\nc{\blambda}{\mbox{\boldmath{$\lambda$}}} 
\nc{\bmu}{ \mbox{\boldmath{$\mu$}}} 
\nc{\boldnu}{ \mbox{\boldmath{$\nu$}}} 
\nc{\bOm}{ \mbox{\boldmath{$\Omega$}}} 
\nc{\bOmega}{ \mbox{\boldmath{$\Omega$}}} 
\nc{\bom}{ \mbox{\boldmath{$\omega$}}} 
\nc{\bomega}{ \mbox{\boldmath{$\omega$}}} 
\nc{\bpi}{ \mbox{\boldmath{$\pi$}}} 
\nc{\bPi}{ \mbox{\boldmath{$\Pi$}}} 
\nc{\bpsi}{ \mbox{\boldmath{$\psi$}}} 
\nc{\bPsi}{ \mbox{\boldmath{$\Psi$}}} 
\nc{\bphi}{ \mbox{\boldmath{$\phi$}}} 
\nc{\bPhi}{ \mbox{\boldmath{$\Phi$}}} 
\nc{\bxi}{ \mbox{\boldmath{$\xi$}}} 
\nc{\bXi}{ \mbox{\boldmath{$\Xi$}}} 
\nc{\bSig}{\mbox{\boldmath{$\Sigma$}}}
\nc{\bSigma}{\mbox{\boldmath{$\Sigma$}}}
\nc{\bsig}{\mbox{\boldmath{$\sigma$}}}
\nc{\bsigma}{\mbox{\boldmath{$\sigma$}}}
\nc{\btau}{\mbox{\boldmath{$\tau$}}}
\nc{\bThe}{\mbox{\boldmath{$\Theta$}}}
\nc{\bTheta}{\mbox{\boldmath{$\Theta$}}}
\nc{\bthe}{\mbox{\boldmath{$\theta$}}}
\nc{\btheta}{\mbox{\boldmath{$\theta$}}}
\nc{\bzeta}{\mbox{\boldmath{$\zeta$}}}
\nc{\bIm}{\mbox{\boldmath{$\Im$}}}



%\nc{\bA}{ \mbox{\boldmath{$A$}}}
%\nc{\bB}{ \mbox{\boldmath{$B$}}}
%\nc{\bb}{ \mbox{\boldmath{$b$}}}
%\nc{\bc}{ \mbox{\boldmath{$c$}}}
%\nc{\bC}{ \mbox{\boldmath{$C$}}}
%\nc{\bd}{ \mbox{\boldmath{$d$}}}
%\nc{\be}{ \mbox{\boldmath{$e$}}}
%\nc{\bh}{ \mbox{\boldmath{$h$}}}  
%\nc{\bH}{ \mbox{\boldmath{$H$}}}  
%\nc{\bI}{ \mbox{\boldmath{$I$}}}  
%\nc{\bJ}{ \mbox{\boldmath{$J$}}}  
%\nc{\bn}{ \mbox{\boldmath{$n$}}}
%\nc{\bP}{ \mbox{\boldmath{$P$}}}
%\nc{\br}{ \mbox{\boldmath{$r$}}}
%\nc{\bR}{ \mbox{\boldmath{$R$}}}
%\nc{\bs}{ \mbox{\boldmath{$s$}}}  
%\nc{\bS}{ \mbox{\boldmath{$S$}}} 
%\nc{\bT}{ \mbox{\boldmath{$T$}}} 
%\nc{\bt}{ \mbox{\boldmath{$t$}}} 
%\nc{\bu}{ \mbox{\boldmath{$u$}}} 
%\nc{\bU}{ \mbox{\boldmath{$U$}}}  
%\nc{\bv}{ \mbox{\boldmath{$v$}}}
%\nc{\bV}{ \mbox{\boldmath{$V$}}}  
%\nc{\bW}{ \mbox{\boldmath{$W$}}}  
%\nc{\bw}{ \mbox{\boldmath{$w$}}}  
%\nc{\bx}{ \mbox{\boldmath{$x$}}}
%\nc{\bX}{ \mbox{\boldmath{$X$}}}
%\nc{\by}{ \mbox{\boldmath{$y$}}} 
%\nc{\bY}{ \mbox{\boldmath{$Y$}}}  
%\nc{\bz}{ \mbox{\boldmath{$z$}}} 
%\nc{\bZ}{ \mbox{\boldmath{$Z$}}}  

\nc{\ba}{ { \bf a }}
\nc{\bA}{ { \bf A }}
\nc{\bB}{ { \bf B }}
\nc{\bb}{ { \bf b }}
\nc{\bc}{ { \bf c }}
\nc{\bC}{ { \bf C }}
\nc{\bD}{ { \bf D }}
\nc{\bd}{ { \bf d }}
\nc{\be}{ { \bf e }}
\nc{\bF}{ { \bf F }}
\nc{\boldf}{ { \bf f }}
\nc{\bG}{ { \bf G }}
\nc{\bh}{ { \bf h }}  
\nc{\bH}{ { \bf H }}  
\nc{\bI}{ { \bf I }}  
\nc{\bJ}{ { \bf J }}  
\nc{\bk}{ { \bf k }}  
\nc{\bK}{ { \bf K }}  
\nc{\bL}{ { \bf L }}
\nc{\bM}{ { \bf M }}
\nc{\bn}{ { \bf n }}
\nc{\bO}{ { \bf O }}
\nc{\bP}{ { \bf P }}
\nc{\bp}{ {\bf p }}
\nc{\br}{ { \bf r }}
\nc{\bR}{ { \bf R }}
\nc{\bolds}{ { \bf s }}  
\nc{\bS}{ { \bf S }} 
\nc{\bT}{ { \bf T }} 
\nc{\bt}{ { \bf t }} 
\nc{\bu}{ { \bf u }} 
\nc{\bU}{ { \bf U }}  
\nc{\bv}{ { \bf v }}
\nc{\bV}{ { \bf V }}  
\nc{\bW}{ { \bf W }}  
\nc{\bw}{ { \bf w }}  
\nc{\bx}{ { \bf x }}
\nc{\bX}{ { \bf X }}
\nc{\by}{ { \bf y }} 
\nc{\bY}{ { \bf Y }}  
\nc{\bz}{ { \bf z }} 
\nc{\bZ}{ { \bf Z }}  

% -- distribution functions
\nc{\YR}{[\bY,R]}
\nc{\YgivenR}{[\bY \mid R]}
\nc{\RgivenY}{[R \mid \bY]}
\nc{\Y}{[\bY]}
\nc{\R}{[R]}




% --- spline models
\nc{\dio}{d_i^o}
\nc{\timi}{t_{i,m_i}}
\nc{\betahat}{\hat{\bbet}}
%\nc{\pihat}{\hat{\pi}}
\nc{\mui}{\bmu_{\rm I}}
\nc{\mue}{\bmu^{\rm E}}
\nc{\mup}{\bmu^{\rm P}}
\nc{\muihat}{\hat{\bmu}_{\rm I}}
\nc{\muehat}{\hat{\bmu}^{\rm E}}
\nc{\muphat}{\hat{\bmu}^{\rm P}}
\nc{\delhat}{\hat{\bdel}}
\nc{\muhat}{\hat{\bmu}}

% --- distributions
\nc{\iid}{\stackrel{\rm iid}{\sim}}
\nc{\law}{\stackrel{\scl}{=}}


% --- u-statistics 
\nc{\phiij}{ \phi_{ij}( \Delta_0) }
\nc{\phiiprmj}{ \phi_{i'j}( \Delta_0) }
\nc{\phiijprm}{ \phi_{ij'}( \Delta_0) }
\nc{\phixy}{ \phi( X_i(S_{ik}), Y_j(T_{jl}) ) }
\nc{\phixydo}{ \phi( X_i(S_{ik}), Y_j(T_{jl})-\Delta_0 ) }
\nc{\phixyd}{ \phi( X_i(S_{ik}), Y_j(T_{jl})-\Delta) }
\nc{\phixydstar}{ \phi^*( X_i(S_{ik}), Y_j(T_{jl})-\Delta) }
\nc{\phixystdttil}{ \tilde{\phi}( X_i(s), Y_j(t)-\Delta, \theta) }
\nc{\phixydttil}{ \tilde{\phi}( X_i(S_{ik}), Y_j(T_{jl})-\Delta, \theta) }
\nc{\Nmn}{{\sqrt{N} \over mn}}

\nc{\Xis}{X_i(s)}
\nc{\Yjt}{Y_j(t)}

%\nc{\sumjprime}{\sum_{j'=1 \\ j' \neq j}^n}
%\nc{\sumiprime}{\sum_{i'=1 \\ i' \neq i}^m}

% --- hats
\nc{\bthehat}{\hat{\bthe}}

% --- tildes
\nc{\Ritil}{\tilde{R}_i}







\nc{\Ybar}{\overline{Y}}
\nc{\Rbar}{\overline{R}}
\nc{\Nbar}{\overline{N}}
\nc{\intzeroinf}{\int_0^\infty}

\nc{\Fhat}{\hat{F}}
\nc{\Ghat}{\hat{G}}

\nc{\FhatS}{\hat{F}(S_{ik})}
\nc{\GhatT}{\hat{G}(T_{jl})}

\nc{\Fhatik}{\hat{F}_{ik}}
\nc{\Ghatjl}{\hat{G}_{jl}}
\nc{\Fik}{F_{ik}}
\nc{\Gjl}{G_{jl}}
\nc{\phiijkl}{\phi_{ik,jl}(\Delta)}
\nc{\phiijkltil}{\tilde{\phi}_{ik,jl}(\Delta_0,\theta_0)}
\nc{\ord}{N^{-3/2}}           % --- effective order of summation           
\nc{\sumijkl}{\sum_{ijkl}}

\nc{\Citil}{\tilde{C}_i}
\nc{\Crtil}{\tilde{C}_r}
\nc{\Djtil}{\tilde{D}_j}
\nc{\Ditil}{\tilde{D}_i}

\nc{\Cithe}{\tilde{C}^{\theta}_i}
\nc{\Djthe}{\tilde{D}^{\theta}_j}

\nc{\Sikthe}{S_{ik}^{\theta}}
\nc{\Tjlthe}{T_{jl}^{\theta}}


% --- cressie notation (image analysis)
\nc{\Zi}{ \bZ_{-i}}
\nc{\zic}{ \lbc z(\bs_j) \: : \: i \neq j \rbc }
\nc{\zkap}{ \bz_{\kappa} }
\nc{\sumi}{ \sum_i }
\nc{\sumj}{ \sum_j }
\nc{\sumij}{ \sum_{i < j} }
\nc{\sumiandj}{ \sum_{i, j} }
\nc{\zsi}{ z(\bs_i) }
\nc{\Zsi}{ Z(\bs_i) }
\nc{\zsj}{ z(\bs_j) }
\nc{\zsn}{ z(\bs_n) }
\nc{\zsone}{ z(\bs_1) }
\nc{\pZ}{ \Pr \lbc \bZ \rbc }
\nc{\qz}{ Q( \bz ) }
\nc{\qZ}{ Q( \bZ ) }
 

% mixture and selection models 
\nc{\thetaYD}{\theta_{Y\mid D}}
\nc{\thetaD}{\theta_D}
\nc{\psiDY}{\psi_{D\mid Y}}
\nc{\psiY}{\psi_Y}




% missing data notations
\nc{\tn}{\Theta^{\nu}}
\nc{\Etn}{E_{\theta^{\nu}}}
\nc{\tnone}{\Theta^{\nu+1}}
\nc{\Lm}{L_{\text{m}}}
\nc{\Lo}{L_{\text{o}}}
\nc{\Ym}{Y_{\text{m}}}
\nc{\Yo}{Y_{\text{o}}}
\nc{\ym}{y_{\text{m}}}
\nc{\yo}{y_{\text{o}}}


\nc{\vijb}{v_{ij} - \bX_{i(j)}  \bbet}
\nc{\vikb}{v_{ik} - \bX_{i(k)}  \bbet}
\nc{\vilb}{v_{il} - \bX_{i(l)}  \bbet}
\nc{\betart}{ \bbet^{(r)}_{t_i} }
\nc{\betarj}{ \bbet^{(r)}_j } 
\nc{\yij}{y_{ij}}
\nc{\Xmisi}{ {\bX_{ i{\rm (mis)} }} }
\nc{\Xobsi}{ {\bX_{ i{\rm (obs)} }} }
\nc{\Zobsi}{ {\bZ_{ i{\rm (obs)} }} }
\nc{\bSigobs}{ \bSig_{  {\rm obs} } }
\nc{\bSigmis}{ \bSig_{  {\rm mis} } }
\nc{\bSigmo}{ \bSig_{  {\rm mis,obs} } }
\nc{\bSigom}{ \bSig_{  {\rm obs,mis} } }
\nc{\Xil}{{\bX}_{il}}
\nc{\Zil}{{\bZ}_{il} }
\nc{\omilr}{\omega_{il}^{(r)}}
\nc{\delio}{\bdel_i^{{\rm obs}} }

\nc{\obs}{{\text{obs}}}
\nc{\mis}{{\text{mis}}}
\nc{\rep}{{\text{rep}}}


\nc{\yio}{ {y_i^{\rm o} }}
%\nc{\Yo}{ {Y^{\rm o} }}
\nc{\Yio}{ {Y_i^{\rm o }} }
%\nc{\Ym}{ {Y_^{\rm m} }}
\nc{\Yim}{ {Y_i^{\rm m} }}
\nc{\yim}{ {y_i^{\rm m} }}
%\nc{\yo}{ {y^{\rm o} }}
%\nc{\ym}{ {y^{\rm m}}}
\nc{\Yc}{Y^{\rm c}}
\nc{\Yic}{Y_i^{\rm c}}
\nc{\yc}{y^{\rm c}}
\nc{\yic}{y_i^{\rm c}}
%\nc{\Yobsi}{{\bf Y}_{i,{\rm obs}}}
%\nc{\Ymisi}{{\bf Y}_{i,{\rm mis}}}
%\nc{\yobsi}{{\bf y}_{i,{\rm obs}}}
%\nc{\ymisi}{{\bf y}_{i,{\rm mis}}}
%\nc{\ymis}{{\bf y}_{{\rm mis}}}
%\nc{\yobs}{{\bf y}_{\text{ obs}}}

\nc{\yi}{y_i}
\nc{\Yi}{Y_i}

\nc{\fyic}{f ( \yic ; \; \psiY )}
\nc{\fyi}{f ( y_i ; \; \psiY ) }
\nc{\fdigivenyic}{f ( d_i  \mid  \yic ; \; \psiDY )}
\nc{\fditilgivenyic}{f ( \tilde{d}_i  \mid  \yic ; \; \psiDY )}
\nc{\fditilgivenyi}{f ( \tilde{d}_i  \mid  \yi ; \; \psiDY )}
\nc{\Fditilgivenyic}{F ( \tilde{d}_i  \mid  \yic ; \; \psiDY )}
\nc{\Fditilgivenyi}{F ( \tilde{d}_i  \mid  \yi ; \; \psiDY )}
\nc{\fdigivenyi}{f (d_i \mid y_i ; \;  \psiDY  )}
\nc{\fyicdi}{f \left( \yic, d_i \right)}
\nc{\fyidi}{f \left( \yi, d_i \right)}

\nc{\fymidr}{f_{Y \mid R}}
\nc{\fyr}{f_{Y,R}}
\nc{\frmidy}{f_{R \mid Y}}
\nc{\fy}{f_Y}
\nc{\fr}{f_R}


\nc{\fyicgivendi}{f (\yic \mid d_i; \; \thetaYD )}
\nc{\fyigivendi}{f (\yi \mid d_i; \; \thetaYD )}
\nc{\fyicgivens}{f (\yic \mid s; \; \thetaYD )}
\nc{\fyigivens}{f (\yi \mid s; \; \thetaYD )}
\nc{\fdi}{f ( d_i; \; \thetaD )}

\nc{\fyicX}{f ( \yic \mid X_i; \; \psiY )}
\nc{\fyiX}{f ( y_i \mid X_i; \; \psiY ) }
\nc{\fdigivenyicX}{f ( d_i  \mid  \yic, X_i ; \; \psiDY )}
\nc{\fdigivenyiX}{f (d_i \mid y_i, X_i ; \;  \psiDY  )}
\nc{\fyicdiX}{f \left( \yic, d_i \mid X_i \right)}

\nc{\fyicgivendiX}{f (\yic \mid d_i, X_i; \; \thetaYD )}
\nc{\fyigivendiX}{f (y_i \mid d_i, X_i; \; \thetaYD )}
\nc{\fdiX}{f ( d_i \mid X_i; \; \thetaD )}

\nc{\Yistar}{\bY_i^*}

\nc{\Dio}{D_i^{\rm obs}}
\nc{\bdelio}{\bdel_{ i \, {\rm (obs)}} }

\nc{\fygivend}{f_{Y \mid \delta}}
\nc{\fyd}{f_{Y, \delta}}
\nc{\fd}{f_\delta}
\nc{\FD}{F_D}
\nc{\fygivenbd}{f_{Y\mid b, \delta}}

\nc{\alphahat}{\hat{\bal}}
\nc{\phihat}{\hat{\bphi}}
%\nc{\pihat}{\hat{\bpi}}
\nc{\thetahat}{\hat{\bthe}}
\nc{\thetatilde}{\tilde{\bthe}}
\nc{\scoretheta}{\bS(\bthe; \, \scc)}
\nc{\hesstheta}{\bH(\bthe; \, \scc)}
\nc{\infotheta}{\sci(\bthe; \, \scc)}
\nc{\sitheta}{\bs_i(\bthe; \, \scc_i)}
\nc{\sithetahat}{\bs_i(\thetahat; \, \scc_i)}

\nc{\loglikobs}{\ell_{{\rm o}}(\bthe; \, \sco)}
\nc{\scoreobs}{\bS_{{\rm o}}(\bthe; \, \sco)}
\nc{\hessobs}{\bH_{{\rm o}}(\bthe; \, \sco)}
\nc{\infoobs}{\scj_{{\rm o}}(\bthe; \, \sco)}

\nc{\Cil}{\scc_{il}}
\nc{\olog}{\lambda^*(\bthe, \Xobs)}
\nc{\LthetaC}{\scl(\bthe; \, \scc)}
\nc{\LthetaCi}{\scl_i(\bthe; \, \scc_i)}
\nc{\LthetaCil}{\scl_i (\bthe; \, \scc_{il}) }
\nc{\lthetaC}{\ell(\bthe; \, \scc)}
\nc{\lthetaCi}{\ell_i(\bthe; \, \scc_i)}
\nc{\lthetaCil}{\ell_i (\bthe; \, \scc_{il}) }
\nc{\Qtheta}{\scq \left( \bthe \, \left| \,  \bthe^{(r)} \right. \right)}
\nc{\thetar}{\bthe^{(r)}}
\nc{\thetas}{\bthe^{(s)}}
\nc{\alphas}{\bal^{(s)}}
\nc{\psis}{\psi^{(s)}}
\nc{\alphasplusone}{\bal^{(s+1)}}
\nc{\psisplusone}{\bpsi^{(s+1)}}
\nc{\alphapsis}{\left( \alphas, \psis \right)}

\nc{\thetarplusone}{\bthe^{(r+1)}}
\nc{\ologi}{\lambda^*_i(\bthe, \Xobs)}
\nc{\llogi}{\lambda_i \left( \bthe, \tilde{\Xcom}_{il} \right) }

\nc{\scxil}{\tilde{\Xcom}_{il}} 
\nc{\siginv}{\bSig_i^{-1}}

\nc{\fofym}{ f \left( \by_i \mid \bbet_m, \bSig \right) }
\nc{\mphim}{ \phi_M \lsq \bSig^{-1/2}(\by_i - \bX_i \bbet_m) \rsq }
\nc{\mphit}{ \phi_M \lsq \bSig^{-1/2}(\by_i - \bX_i \bbet_{t_i}) \rsq }
\nc{\mphij}{ \phi_M \lsq \bSig^{-1/2}(\by_i - \bX_i \bbet_j) \rsq }
\nc{\mphik}{ \phi_M \lsq \bSig^{-1/2}(\by_i - \bX_i \bbet_k) \rsq }
\nc{\expkerm}{ \exp  \lbc -\half \bu_i(\bbet_m)' \bSig^{-1} \bu_i(\bbet_m)
  \rbc } 
\nc{\expkerk}{ \exp  \lbc -\half \bu_i(\bbet_k)' \bSig^{-1} \bu_i(\bbet_k)
  \rbc } 
\nc{\expkerj}{ \exp  \lbc -\half \bu_i(\bbet_j)' \bSig^{-1} \bu_i(\bbet_j)
  \rbc } 
\nc{\normscorem}{\left( \bX_i' \bSig^{-1} \bX_i \bbet_m - \bX_i' \bSig^{-1}
  \by_i \right) } 
\nc{\normscorej}{\left( \bX_i' \bSig^{-1} \bX_i \bbet_j - \bX_i' \bSig^{-1}
  \by_i \right) } 
\nc{\piti}{ \pi \left( t_i, \bal, \bZ_i\bgam \right) }
\nc{\omij}{ \om_{ij} \left( t_i, \bal, \bZ_i\bgam \right) }
\nc{\phibetak}{ \phi_M(\bbet_k) }
\nc{\phibetaj}{ \phi_M(\bbet_j) }
\nc{\dphidbetak}{ \left. \dpl \phibetak \right/ \dpl \bbet_k }
\nc{\dphidbetakf}{ \frac{ \dpl \phibetak }{ \dpl \bbet_k } }
\nc{\uik}{\bu_i \left( \bbet_k  \right)}
\nc{\mset}{ \{ 0, 1, \ldots, M \} }
\nc{\betasigma}{ \left( \lbc \bbet^{(r)}_t \rbc, \bSig^{(r)} \right) }
\nc{\Thetar}{ \bThe^{(r)} }


% --- kaplan meier and survival
\nc{\shatkm}{\hat{S}_{\rm KM}}

% --- environs
\nc{\ds}{\displaystyle}

\nc{\beq}{\begin{eqnarray*}}
\nc{\eeq}{\end{eqnarray*}}

\nc{\beqna}{\begin{eqnarray}}
\nc{\eeqna}{\end{eqnarray}}

\nc{\bct}{\begin{center}}
\nc{\ect}{\end{center}}

\nc{\bds}{\begin{description}}
\nc{\eds}{\end{description}}

\nc{\bit}{\begin{itemize}}
\nc{\eit}{\end{itemize}}
 
\nc{\bnu}{\begin{enumerate}}
\nc{\enu}{\end{enumerate}}

\nc{\bgt}{\begin{table}}
\nc{\bgtb}{\begin{center} \begin{tabular}}
\nc{\entb}{\end{tabular} \end{center} }
\nc{\ent}{\end{table}}

\nc{\ts}{\textstyle}













  


% Local Variables: 
% mode: latex
% TeX-master: t
% End: 
